Answer:
[tex]\large\boxed{1.\ the\ slope\ is\ \dfrac{1}{4}}\\\boxed{2.\ y=3x-5}\\\boxed{3.\ (3, 6)}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_2}\\\\l\ \parallel\ k\iff m_1=m_2\\\\m-slope\\b-y-intercept\to(0,\ b)\\\\1.\\\\y=-4x+1\to m_1=-4\\\\m_2=-\dfrac{1}{-4}=\dfrac{1}{4}[/tex]
[tex]2.\\y=3x+2\to m_1=3\\\\m_2=3,\ b=-5\\\\y=3x-5[/tex]
[tex]\text{Calculate}\ a\ \text{and}\ b:\\\\a=\dfrac{6-(-9)}{5}=\dfrac{15}{5}=3\\\\b=\dfrac{8-(-2)}{5}=\dfrac{10}{5}=2\\\\\text{Calculate the coordinates of a point:}\\\\x=-9+4a\to x=-9+4(3)=-9+12=3\\\\y=-2+4b\to y=-2+4(2)=-2+8=6[/tex]
